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Q.

The ratio of wavelength of a Photon and that of an electron of same energy will be

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a

$sqrt {frac{{2m}}{E}}$

b

$sqrt {frac{E}{{2m}}}$

c

$csqrt {frac{{2m}}{E}}$

d

$sqrt {frac{{Ec}}{{2m}}}$

answer is C.

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Detailed Solution

${E_{photon}} = E = PC$

$E = frac{{hC}}{{{lambda _{photon}}}}$

${lambda _{photon}} = frac{{hC}}{E}.....(1)$

${E_{electron}} = E = frac{{{p^2}}}{{2m}} Rightarrow p = sqrt {2mE}$

${lambda _{electron}} = frac{h }{{sqrt {2mE} }}.....(2)$

$frac{left ( 1right )}{left ( 2 right )} = frac{{{lambda _{photon}}}}{{{lambda _{electron}}}} = frac{{Csqrt {2mE} }}{E} = Csqrt {frac{{2m}}{E}}$

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